Manchester United will play Midtjylland, the Danish champions, in the last 32 of the Europa League following draw in Nyon, with Liverpool facing Augsburg and Tottenham Hotspur taking on Fiorentina.

United travel to the MCH Arena in Herning for the first leg on 18 February, with Jess Thorup’s team at Old Trafford a week later.

The Champions League defeat against Wolfsburg last week consigned United to Europe’s second tier club competition – they were previously in the Europa League three years ago, when Athletic Bilbao knocked them out at the last-16 stage, 5-3 on aggregate.

Midtjylland were formed only in 1999 and last year’s domestic title triumph was their first, having finished second twice, in 2007 and 2008. United have faced Danish opposition three times, all in the Champions League, playing Brondby in 1998, Copenhagen in 2006 and Aalborg in 2008.

Thorup said: “Miracles have happened before, and we will probably need one again. However, we do not just lie down. We deserved to qualify for the round of 32, and we aim to prove that to ourselves and to our opponents.”

Mikkel Andersen, Midtjylland’s goalkeeper, said: “This is as big as it gets. Of course, we have a chance against Manchester United. We can play without any pressure.” Midtjylland are third in the league, four points behind Copenhagen.

Liverpool’s draw with Augsburg – they play the opening leg away – means Jürgen Klopp will return to his homeland.

Markus Weinzierl, the Augsburg coach since 2012, said: “We are happy. We will give it everything. This game is something special. Liverpool are cult, Jürgen Klopp is a huge name in Germany too. Klopp knows us and will not underestimate us. We will be outsiders against Liverpool but are gladly accepting that role.”

Paul Verhaegh, the Augsburg defender, said: “We have already proven against Dortmund in the Bundesliga that we are capable of causing an upset. We now want to repeat that against Liverpool. Anfield – that’s football history. We were wishing for something like this and of course that’s great.” Augsburg are 13th in the Bundesliga, only two points above the relegation zone.

Tottenham have the toughest draw of the three English clubs, having to play Fiorentina, who are second in Serie A and who knocked them out of the Europa League last season, four points behind Internazionale. Mauricio Pochettino’s team have the advantage of being at home in the second leg.

Europa League round of 32 draw

Valencia v Rapid Vienna

Fiorentina v Tottenham

Borussia Dortmund v Porto

Fenerbahce v Lokomotiv Moscow

Anderlecht v Olympiacos

Midtjylland v Manchester United

Augsburg v Liverpool

Sparta Prague v Krasnodar

How Midtjylland took the analytical route towards the Champions League